Rewrite as a simplified fraction. ${3.65\overline{8} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 3658.8888...\\ 100x &= 365.8888...\end{align*}}$ Subtracting the two equations, we have: ${900x = 3293}$ ${x = \dfrac{3293}{900}} \text{or} {3 \dfrac{593}{900}}$